simulation of electromagnetic heating of cryopreserved samples

Simulation of Simulation of Electromagnetic Electromagnetic

Heating of Heating of Cryopreserved Cryopreserved

SAMPLESSAMPLESC. C. LuC. C. Lu

Department of Electrical and Computer Department of Electrical and Computer EngineeringEngineering

University of KentuckyUniversity of Kentucky

Lexington, KY 40506Lexington, KY 40506

*

University of KentuckyUniversity of Kentucky 22

OUTLINEOUTLINE

INTRODUCTIONINTRODUCTION FORMULATION OF EM AND HEAT FORMULATION OF EM AND HEAT

TRANSFER ANALYSISTRANSFER ANALYSIS IMPLEMENTATIONIMPLEMENTATION SIMULATION RESULTSSIMULATION RESULTS SUMMARYSUMMARY


INTRODUCTION (1)INTRODUCTION (1)CRYOPRESERVATION STEPSCRYOPRESERVATION STEPS

SAMPLE PROCESS (CPA FILLING)SAMPLE PROCESS (CPA FILLING) COOL SAMPLE TO LOW TEMPERATURECOOL SAMPLE TO LOW TEMPERATURE PRESERVE SAMPLE IN LOW PRESERVE SAMPLE IN LOW

TEMPERATURE STATUSTEMPERATURE STATUS WORM THE SAMPLE TO ROOM WORM THE SAMPLE TO ROOM

TEMPERATURE (REWARMINGTEMPERATURE (REWARMING POSTPROCESSINGPOSTPROCESSING


INTRODUCTION (2)INTRODUCTION (2)SYSTEM CONFIGURATIONSYSTEM CONFIGURATION

Microwave Source

Cavity

Sample

Liquid Nitrogen

Temperature monitor


INTRODUCTION (2)INTRODUCTION (2)

Rewarming requirements for minimum Rewarming requirements for minimum tissue damagetissue damage Small temperature gradient: Small temperature gradient: uniformuniform High warming rate: High warming rate: rapidrapid

Using microwave for rewarmingUsing microwave for rewarming: : Volumetric heating: EM energy is Volumetric heating: EM energy is

delivered to every point in a sampledelivered to every point in a sample Rapid warming is realized by very high E-Rapid warming is realized by very high E-

field intensity in a resonant cavityfield intensity in a resonant cavity


INTRODUCTION (3)INTRODUCTION (3)

DifficultiesDifficulties Thermal runaway (hot spot absorbs more Thermal runaway (hot spot absorbs more

power and gets even hotter)power and gets even hotter) Conflicting controls: Conflicting controls: uniformityuniformity requires low requires low

frequency fields (deeper penetration), frequency fields (deeper penetration), rapidrapid heating requires high frequency fieldheating requires high frequency field

SolutionsSolutions Trade-off in selection of resonant frequencyTrade-off in selection of resonant frequency Control of field patternControl of field pattern Selection of right cryoprotectant agent (CPA)Selection of right cryoprotectant agent (CPA)


Methods to study microwave Methods to study microwave rewarming for rewarming for

cryopreservationcryopreservation Experimental studiesExperimental studies

Realistic modelingRealistic modeling Validation of theory and numerical codesValidation of theory and numerical codes

Numerical studiesNumerical studies Ideal configurationIdeal configuration High accuracyHigh accuracy Easy to search optimum warming conditionsEasy to search optimum warming conditions Results used as guidelines for system designResults used as guidelines for system design


IMPORTANT FACTORS IMPORTANT FACTORS AFFACTING REWARMING AFFACTING REWARMING

PROCESSPROCESS Microwave frequencyMicrowave frequency Cavity shapeCavity shape Complex permittivity of CPA and its Complex permittivity of CPA and its

temperature dependencytemperature dependency Size and Shape of sample under testSize and Shape of sample under test


OPTIMIZATION OF REWARMING OPTIMIZATION OF REWARMING PROCESSPROCESS

GIVENGIVEN: Maximum allowed temperature : Maximum allowed temperature gradientgradient

SEARCHSEARCH: Control parameters to realize : Control parameters to realize maximum warming ratemaximum warming rate

METHODMETHOD: Numerical solution of the EM : Numerical solution of the EM equations and the heat transfer equationequations and the heat transfer equation


MAXWELL’S EQUATION SOLVER

HEAT TRANSFER EQUATION SOLVER

Heat Source

EM Source

, ,

, ,k C

( )T r

,E H

SIMULATION DIAGRAM


PREVIOUS WORKSPREVIOUS WORKS

Separate EM and heat transfer solutionSeparate EM and heat transfer solution FEM for heat transfer and approximate FEM for heat transfer and approximate

EM solution (D. Chen and Singh, 1992)EM solution (D. Chen and Singh, 1992) Heating pattern analysis using spheres Heating pattern analysis using spheres

(X. Bai and D. Pegg, 1992)(X. Bai and D. Pegg, 1992) Combined analysis:Combined analysis:

FDTD: Ma, et al (1995), FDTD: Ma, et al (1995), Torres and Jacko (1997)Torres and Jacko (1997) X. Han (2004)X. Han (2004)


EM SOLUTION METHODS EM SOLUTION METHODS

FDTD, FEM, MOM can all be FDTD, FEM, MOM can all be applied for the simulationapplied for the simulation FDTDFDTD: Time consuming for resonant : Time consuming for resonant

frequency search, and long iteration frequency search, and long iteration for CW sourcefor CW source

FEMFEM: Difficult for mesh generating, : Difficult for mesh generating, slow convergenceslow convergence

MOMMOM: Efficient and accurate (sample : Efficient and accurate (sample size is normally electrically small). size is normally electrically small). Easy for mesh generation.Easy for mesh generation.


PRESENT WORK PRESENT WORK

Combined EM and heat transfer Combined EM and heat transfer solution.solution.

Hexahedron grid and Roof-top Hexahedron grid and Roof-top basis function for EM solutionbasis function for EM solution

Hexahedron grid and control Hexahedron grid and control volume for heat transfer solutionvolume for heat transfer solution

Temperature varying electrical and Temperature varying electrical and thermal parameters for samples.thermal parameters for samples.


THE INTEGRAL EQUATIONS THE INTEGRAL EQUATIONS (EM)(EM)

G r r Ik

r r

r r, '

exp | ' |

| ' |a f k p FH IK

1

42

sca ( ) ( , ') ( ) ' ( , ') ( ) 'V S

V S

E r i G r r J r dV i G r r J r dS

( ) ( ) ( ), Samplesca incE r E r E r r

( ) ( )V bJ r i E r

tan tan( ) ( ) ( ) , Wallsca incE r E r E r r


MODEL REPRESENTATIONMODEL REPRESENTATION Hexahedron cells (quadrangle faces)Hexahedron cells (quadrangle faces) Well connected meshWell connected mesh

Using rectilinear hexahedrons, it is possible to accurately model any arbitrarily shaped solid dielectrics.


IE DISCRETIZATIONIE DISCRETIZATION

( ) ( , ') ( ') 'i j

ij i jV VA t r G r r f r dr dr

Matrix elements for near-neighbor basis and testing functions

Testing function

Basis function

/ 1 , Sample

1, Wall

j

i

bi

t

f

r

r

2( ) ( , ') ' ( , ') ' '

i j jij b i j jV V V

b

A i t r g r r f dr g r r f dr drk

In mixed-potential format:

Short dipole as excitation source


HEAT TRANSFER SOLUTIONHEAT TRANSFER SOLUTION

Heat transfer equationHeat transfer equation

Heat source (EM field)Heat source (EM field)

Discretization: Controlled volume method Discretization: Controlled volume method (time explicit approach)(time explicit approach)

( )T

C k T q rt

2 31( ) ( ) , (W/m )

2q r E r

1

O ( )i

n ni i

i i

V

T TV C k T dS q r V

t



The traditional control volume methodThe traditional control volume method

11/ 2

i

i ii y z

xV

T Tk T dS k

Ti Ti+1

x

Applies to rectlinear grids only!



Sampling point

Part of a Control Volume

A hexahedron volume cell (arbitrarily shaped 6-sided volume unit)—easy to model objects with curved boundaries.

Temperatures are sampled at the vertices of the hexahedron

A control volume is set for each sampling point

Boundary condition: dT/dn=(Tf-T)h


CONTROL VOLUME METHODCONTROL VOLUME METHOD(2D VIEW)(2D VIEW)

Sampling point

Control Volume (enclosed by dash lines): flow through the RED dashed boundary is calculated for each sample point

Boundary condition is used to evaluate the head flow on boundary elements


VALIDATION OF EM CODE VALIDATION OF EM CODE FIELD IN A DIELECTRIC SPHEREFIELD IN A DIELECTRIC SPHERE

0.15m, 3.3 1 , 300MHzrR i f Parameters:

EXACT NUMERICAL

Incident Direction


VALIDATION OF EM CODEVALIDATION OF EM CODEFIELD IN A DIELECTRIC SPHERICAL FIELD IN A DIELECTRIC SPHERICAL

SHELLSHELL

0.04m, 0.01m, 64.56 0.5 , 300MHzrR t i f

+ + + + Exact


VALIDATION OF THERMAL VALIDATION OF THERMAL CODE:CODE: TEMPERATURE IN A CUBIC TEMPERATURE IN A CUBIC

SAMPLESAMPLE

Numerical

+ + + + Exact

y

x

z

Cube Size:6cm x 6cm x 6cm

Sample points on x-y Plane


VALIDATION OF THERMAL VALIDATION OF THERMAL CODECODE

TEMPERATURE IN A CUBIC SAMPLETEMPERATURE IN A CUBIC SAMPLE

Numerical

+ + + + Exact

yxz

Time(s)



TEMPERATURE IN A CIRCULAR CYLINDERTEMPERATURE IN A CIRCULAR CYLINDER

yxz



TEMPERATURE IN A SPHERETEMPERATURE IN A SPHERE

yxz


DIELECTRIC MODELDIELECTRIC MODEL

MEASUREMENT FOR FIXED FREQURNCY MEASUREMENT FOR FIXED FREQURNCY AND VARYING TEMPERATURESAND VARYING TEMPERATURES

INTERPOLATION USING MEASUREMENTINTERPOLATION USING MEASUREMENT

INTERPOLATION IS DONE FOR TWO INTERPOLATION IS DONE FOR TWO PHASES (BEFORE AND AFTER PHASE PHASES (BEFORE AND AFTER PHASE CHANGES)CHANGES)


MEASUREMENT OF DIELECTRIC MEASUREMENT OF DIELECTRIC CONSTANTSCONSTANTS

2

110

r

rr kfff

22

0

1

2

11

r

kQQ

Q

fk

fkr

1

1 2

1

2

1

1

2

31

Qfk

k

k

Thermal Meter

ComputerMicrowave Network Analyser

Resonant Cavity

Liquid Nitrogen


MEASUREMENT OF DIELECTRIC MEASUREMENT OF DIELECTRIC CONSTANTSCONSTANTS 2

110

r

rr kfff

22

0

1

2

11

r

kQQ

Q

fk

fkr

1

1 2

1

2

1

1

2

31

Qfk

k

k

Step 1: Measurement of df and dQ for a set of known samples

Step 2: Calculate coefficients: k1 and k2

Step 3: For a sample with unknown permittivity, measure df and dQ

Step 4: Calculate permittivity

Repeat steps 3 and 4 for a new sample (or the same sample at a different temperature (this process is done automatically—controlled by a program).


DIELECTRIC PERMITTIVITY DIELECTRIC PERMITTIVITY MEASUREMENTMEASUREMENT

Negative slop: Good for stablized heating


COMBINED SIMULATIONCOMBINED SIMULATIONSTART

OUTPUT “T” PATTERN

SOLUTION OF WAVE EQUATION: “E” FIELD

SOLUTION OF HEAT TRANSFER EQUATION: “T”

CONVERT “E” TO HEAT SOURCE UPDATE ELECTRICAL AND

THERMAL PARAMETERS

DESIRED “T” PATTERN? NO

YES

1. Try for 5 near-by frequencies:

f0-2*df,

f0-df

f0

f0+df

f0+2*df

2. Interpolate to get new f0

3. Solve for E(f0)


COMBINED SIMULATIONCOMBINED SIMULATION(SOURCE ON VS OFF)(SOURCE ON VS OFF)

yxz

Cavity size: 0.457mx0.3225mx0.5271m

Temperature sampled at corner of a cube with size 6cmx6cmx6cm

Dipole at (-0.13,0,0)

Air temperature is 20 (degs)

24 EM updates

Each update performs 6 solutions (5 trial and 1 actual)

1min per EM solution

144 min total solution time


COMBINED SIMULATIONCOMBINED SIMULATIONFr-TRACK COMPARISONFr-TRACK COMPARISON

yxz



EM source is a dipole at (-0.1,0,0)



COMBINED SIMULATIONCOMBINED SIMULATIONFr vs TIMEFr vs TIME

yxz





Initial frequency of dipole is 428 MHz


COMBINED SIMULATIONCOMBINED SIMULATIONINPUT POWER LEVELINPUT POWER LEVEL

yxz





DIPOLE MOMENT 0.1

DIPOLE MOMENT 0.15


SUMMARYSUMMARY Mixed surface and volume mesh provide Mixed surface and volume mesh provide

flexible modeling of cavities and samples.flexible modeling of cavities and samples. Coupled EM and heat transfer solution Coupled EM and heat transfer solution

simulates the realistic rewarming process.simulates the realistic rewarming process. Simulation results showed thatSimulation results showed that

High power level results in large T-gradientHigh power level results in large T-gradient Resonant frequency tracking increases warming rateResonant frequency tracking increases warming rate CAP concentration level leads to different warming CAP concentration level leads to different warming

performanceperformance

simulation of electromagnetic heating of cryopreserved samples

Documents

em equations

heat transfer solutionfem

approximate em solution

em energy

em solutionhexahedron

rewarming requirements

rewarming processgiven

low temperaturepreserve